Journal ArticleDOI
Numerical inversion of certain laplace transforms by the direct application of fast fourier transform (FFT) algorithm
J.T. Hsu,Joshua S. Dranoff +1 more
TLDR
In this paper, the numerical inversion of Laplace transforms by means of the finite Fourier cosine transform, as presented by Dubner and Abate, was analyzed, and it was found that the proper inversion formula should contain the Fourier sine series as well.About:
This article is published in Computers & Chemical Engineering.The article was published on 1987-01-01. It has received 40 citations till now. The article focuses on the topics: Sine and cosine transforms & Prime-factor FFT algorithm.read more
Citations
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Journal ArticleDOI
The Fourier-series method for inverting transforms of probability distributions
Joseph Abate,Ward Whitt +1 more
TL;DR: This paper reviews the Fourier-series method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions and describes two methods for inverting Laplace transform based on the Post-Widder inversion formula.
Journal ArticleDOI
Extension de la méthode des quadripôles thermiques à l'aide de transformations intégrales—calcul du transfert thermique au travers d'un défaut plan bidimensionnel
TL;DR: The methode des quadripoles, utilisee for diffusion thermique monodimensionnels, is etendue aux cases bi ou tridimensionnel.
Journal ArticleDOI
Analytical solution to an axial dispersion model for the fixed‐bed adsorber
Hsin-Tzu Liao,Ching-Yeh Shiau +1 more
TL;DR: An axial dispersion model for the operation of a fixed-bed adsorber with a linear adsorption isotherm was formulated and solved analytically using the separation of variables method.
Journal ArticleDOI
Parameters estimation and measurement of thermophysical properties of liquids
Benjamin Remy,Alain Degiovanni +1 more
TL;DR: In this article, an experimental bench for the measurement of thermal diffusivity and conductivity of liquids based on a pulsed method is presented, and the entire problem is solved through the thermal quadrupoles method.
Journal ArticleDOI
Graphical method for the calculation of chromatographic performance in representing the trade-off between purity and recovery
TL;DR: A simple engineering framework that enables the rapid representation of the performance of liquid chromatographic separations is provided and can help to identify the optimal operating conditions, in terms of acceptable yield and desired level of contaminant removal, and to redefine the location of product fractions needed to achieve these specifications.
References
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Journal ArticleDOI
An algorithm for the machine calculation of complex Fourier series
J.W. Cooley,John W. Tukey +1 more
TL;DR: Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.
Journal ArticleDOI
A method for the numerical inversion of Laplace transforms
TL;DR: A numerical inversion method for Laplace transforms, based on a Fourier series expansion developed by Durbin [5], is presented in this article, where the disadvantage of the inversion methods of that type, the encountered dependence of discretization and truncation error on the free parameters, is removed by the simultaneous application of a procedure for the reduction of the Discretization error, a method for accelerating the convergence of the Fourier Series and a procedure that computes approximately the "best" choice of the free parameter.
Journal ArticleDOI
Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate's Method
TL;DR: An accurate method is presented for the numerical inversion of Laplace transform, which is a natural continuation to Dubner and Abate's method, and the error bound on the inverse f{t) becomes independent of t, instead of being exponential in t.
Journal ArticleDOI
Numerical Inversion of Laplace Transforms Using a Fourier Series Approximation
TL;DR: A method is presented for numerically inverting a Laplace transform that requires, in addition to the transform function itself, only sine, cosine, and exponential functions and includes a transformation of the approximating series into one that converges very rapidly.
Journal ArticleDOI
Numerical Inversion of the Laplace Transform: A Survey and Comparison of Methods
Brian Davies,Brian Martin +1 more
TL;DR: In this paper, a large number of different methods for numerically inverting the Laplace transform are tested and evaluated according to the criteria of applicability to actual inversion problems, applicability of various types of functions, numerical accuracy, computational efficiency, and ease of programming and implementation.
Related Papers (5)
Numerical Inversion of the Laplace Transform: A Survey and Comparison of Methods
Brian Davies,Brian Martin +1 more
Prediction of breakthrough curves by the application of fast fourier transform
Teh-liang Chen,James T. Hsu +1 more